Abstract

We study inner obstacle problems for a class of strongly degenerate parabolic–hyperbolic quasilinear operators associated with Dirichlet data in an open bounded subset of R p , p ≥ 1 . We first give the definition of a weak entropy solution that warrants uniqueness; the boundary conditions are expressed by using the framework of divergence measure fields. The existence of such a solution is obtained through the vanishing viscosity method.

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